Logic, Logic, and Logic

Logic, Logic, and Logic compiles selected papers and essays by philosopher George Boolos, covering mathematical logic, set theory, and the foundations of mathematics. The collection spans Boolos's career from 1969 to 1996, featuring his work on second-order logic, plural quantification, and the logical paradoxes. The book contains Boolos's influential papers on the iterative conception of sets and his investigations into Gödel's theorems. His writings on the logic of provability form a core part of the text, including his interpretation of Gödel's incompleteness theorems and analysis of modal-logical systems. The essays progress from introductory topics to advanced mathematical concepts, with Boolos maintaining clarity throughout technical discussions. Several papers address fundamental questions about the nature of logic itself and the relationship between logic and mathematics. This collection reveals the intersection of pure logic with broader philosophical questions about truth, knowledge, and the foundations of mathematical reasoning. The work stands as a contribution to both technical logic and the philosophy of mathematics.

Readers consider this a challenging but valuable collection of Boolos' papers on mathematical logic and set theory. The book assumes significant prior knowledge of logic and mathematical notation. Likes: - Clear explanations of complex Gödel theorems - Strong coverage of second-order logic - Inclusion of Boolos' influential work on substitutional quantification - Useful for advanced logic students and researchers Dislikes: - Too technical for beginners - Some papers require specialized mathematical background - A few readers found the organization between sections disjointed - High price point noted by multiple reviewers Ratings: Goodreads: 4.4/5 (23 ratings) Amazon: 4.7/5 (6 ratings) Notable reader comment: "Not for the faint of heart, but Boolos has a gift for making difficult logical concepts precise and understandable once you work through the notation." - Goodreads reviewer The book appears most useful for graduate students and academics rather than general readers seeking an introduction to logic.

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter This exploration of mathematics, symmetry, and recursive structures connects formal logic systems to patterns in art and music through interconnected dialogues and expositions.

Computability and Logic by George S. Boolos, John P. Burgess, and Richard C. Jeffrey The text presents mathematical logic and computability theory through rigorous proofs and fundamental theorems.

Set Theory and Its Logic by Willard Van Orman Quine The book develops set theory from first principles while examining the foundations of mathematics and logical paradoxes.

Mathematical Logic by Joseph Shoenfield This comprehensive treatment covers proof theory, model theory, recursion theory, and set theory with mathematical precision.

The Foundations of Mathematics by Kenneth Kunen The work presents set theory, cardinal arithmetic, and mathematical logic through formal proofs and detailed mathematical constructions.

🔷 George Boolos (1940-1996) taught both mathematics and philosophy at MIT, embodying the intersection between mathematical logic and philosophical reasoning that characterizes his work. 🔷 The book's title "Logic, Logic, and Logic" reflects the three main areas of logic covered: mathematical logic, philosophical logic, and pure logic, with each "logic" representing a distinct approach to the subject. 🔷 Boolos made significant contributions to provability logic and was one of the first to use plural quantification to provide an alternative interpretation of second-order logic. 🔷 The collection includes Boolos's famous paper "Gödel's Second Incompleteness Theorem Explained in Words of One Syllable," which brilliantly explains a complex mathematical concept using only monosyllabic words. 🔷 The book was published posthumously in 1998, edited by Richard Jeffrey, and includes several previously unpublished works, making it a comprehensive collection of Boolos's most important contributions to logic.